Photonic crystal fiber and high-power light transmission system

ABSTRACT

A photonic crystal fiber according to the present invention has a plurality of holes arranged in the optical fiber along a longitudinal direction, in which the holes are arranged such that, in a cross section, a hole ratio which is an area of the holes per unit area is larger in a central side than in an outer side in a portion corresponding to a cladding and that a wide core area can be obtained while the number of modes that can be propagated is limited to several. Moreover, in a high-power optical transmission system according to the present invention, the amount of axis misalignment between the central axis of a laser oscillator and the central axis of the photonic crystal fiber is less than or equal to a certain amount.

TECHNICAL FIELD

The present disclosure relates to a photonic crystal fiber and ahigh-power optical transmission system that enable high power opticaltransmission.

BACKGROUND ART

Along with the progress of high-power lasers, applications to industrialprocessing such as welding using laser light are widely employed.Especially in recent years, high-power fiber lasers having an output ofas high as 10 kW have been developed and are expected to be used formedical and industrial applications. In such a high-power fiber laser,for example as illustrated in Non-Patent Literature 1, the core area isenlarged in a short optical fiber of several meters or less, therebyrelaxing an output power limit due to nonlinearity. Moreover, in laserprocessing, the beam quality of emitted light greatly affects theprocessing efficiency. Since the beam quality strongly depends on a modestate of emitted light, an optical fiber capable of single modetransmission is used in a fiber laser.

Furthermore as illustrated in Non-Patent Literature 2, an optical fiberis coupled to an emitting end of the high-power laser described above,which is applied also to welding processing from a remote place. In thiscase, the beam quality at the emitting end is affected by an excitationstate of a higher order mode in the coupled optical fiber. Therefore,connecting a multimode optical fiber having a large core area as atransmission optical fiber enables transmission of high-power light suchas several kilowatts for several tens of meters or more, however, thebeam quality at the emitting end becomes low. In order to enhance thebeam quality, it is necessary to reduce the number of propagation modes;however, in structure design of the optical fibers in general, reductionof the number of propagation modes and enlargement of a core area are ina trade-off relationship, and thus an attempt to enhance the beamquality results in limiting the power that can be transmitted.

Furthermore as illustrated in Non-Patent Document 3, it is known that,by using a photonic crystal fiber having a hole structure, the trade-offbetween a single mode operation region and enlargement of a core areacan be relaxed as compared with a general optical fiber in which arefractive index distribution is formed by adding a dopant to a core.Therefore, it is known that, in a photonic crystal fiber for acommunication application, deterioration of tradition characteristicsdue to a nonlinear effect can be mitigated in an optical communicationsystem. Furthermore in Patent Literature 1, it is known that thetrade-off between the single mode operation region and enlargement of acore area can be further relaxed as compared with a uniform structure byusing a photonic crystal fiber in which holes are arrangednon-uniformly.

CITATION LIST Patent Literature

-   Patent Literature 1: International Publication WO 2011/093349

Non Patent Literatures

-   Non-Patent Literature 1: Himeno, “Kousyutsuryoku laser no kiso to    tokuchou”, Fujikura Technical Journal, vol. 1, pp. 1-6, January    2014.-   Non-Patent Literature 2: Yamazaki et al., “10 kW Long-length Cables    for Laser Transmission Incorporated with Eight Optical Fibers”, R &    D Review of Mitsubishi Cable Industries, Ltd., No. 105, pp. 24-27,    October 2008.-   Non-Patent Literature 3: Matsui et al., “Photonic Crystal Fiber no    Jikkou Danmenseki Kakudai ni Kansuru Kenntou”, The Institute of    Electronics, Information and Communication Engineers, B-13-21,    September 2008.-   Non-Patent Literature 4: G. P. Agrawal, “Nonlinear Fiber Optics”,    ACADEMIC PRESS. pp. 278-279.

SUMMARY OF INVENTION Technical Problem

As described above, obtaining a wide core area with a small number ofpropagation modes in order to obtain high quality and high output powerwith a long propagation distance is in a trade-off relationship in theconventional optical fibers, and thus there is a problem that high-powerlight having high output and a high quality cannot be obtained.Furthermore, even in the case of using a photonic crystal fiber, inindustrial high-power transmission applications of a kilowatt class farexceeding communication applications, there is a problem that it isunknown how much the trade-off is improved and that structure designsuitable for obtaining high quality and high output power is unclear.

Therefore, in order to solve the above problems, an object of thepresent invention is to provide a photonic crystal fiber in which a widecore area can be obtained with a limited number of propagation modes anda high-power optical transmission system including the photonic crystalfiber and having a high beam quality.

Solution to Problem

According to the present invention, holes of a photonic crystal fiberare arranged such that, in a cross section, a hole ratio, which is anarea of the holes per unit area, is larger in a central side than in anouter side in a portion corresponding to a cladding and that a wide corearea can be obtained while the number of modes that can be propagated islimited to several. Moreover, in a high-power optical transmissionsystem according to the present invention, the amount of axismisalignment between the central axis of a laser oscillator and thecentral axis of the photonic crystal fiber is less than or equal to acertain amount.

Specifically, a first photonic crystal fiber according to the presentinvention is a photonic crystal fiber having a plurality of holesarranged in the optical fiber along a longitudinal direction,

in which, in a cross section, a hole ratio which is an area of the holesper unit area is larger in a central side than in an outer side in aportion corresponding to a cladding,

an interval among all of the holes is Λ, and a diameter d1 of the holesin the central side is larger than a diameter d of the holes in theouter side, and, when Λ is represented in a horizontal axis and d1/d isrepresented in a vertical axis, Λ, d1, and d are in a region whererespective regions represented by mathematical formulas C1 overlap, and

a bending loss of a basic mode is 1 dB/km with a bending radius of 500mm or less.[Mathematical Formulas C1]d1/d≤0.633Λ−5.467(Λ≤11.8 μm)d1/d≤−0.0429Λ+2.486(11.8 μm≤Λ≤15.4 μm)d1/d≥0.0454Λ1.13(Λ≥15.4 μm)d1/d≥1(Λ≤16.8 μm)d1/d≥0.117Λ−0.96(Λ≥16.8 μm)  (C1)

It is preferable that the number of propagation modes of the firstphotonic crystal fiber according to the present invention is three orless in order not to deteriorate the beam quality even in a case whereincident light from a laser oscillator and a mode field diameter of thephotonic crystal fiber are not matched.

Moreover, the first photonic crystal fiber according to the presentinvention enables high power transmission of light and thus does notgenerate output saturation due to stimulated Raman scattering uponpropagation of light of 90 kW·m.

A second photonic crystal fiber according to the present invention is aphotonic crystal fiber having a plurality of holes arranged in theoptical fiber along a longitudinal direction,

in which, in a cross section, a hole ratio which is an area of the holesper unit area is larger in a central side than in an outer side in aportion corresponding to a cladding,

a diameter of all of the holes is d, and an interval Λ1 of the holes inthe central side is smaller than an interval Λ of the holes in the outerside, and, when Λ is represented in a horizontal axis and d/Λ isrepresented in a vertical axis, Λ and d are in a region where respectiveregions represented by mathematical formulas C2 overlap, and a bendingloss of a basic mode is 1 dB/km with a bending radius of 500 mm or less.[Mathematical Formulas C2]d/Λ≤0.24Λ−2.22(Λ≤10.8 μm)d/Λ≤0.00667Λ+0.293(10.8 μm≤Λ≤19.5 μm)d/Λ≤0.01Λ+0.23(Λ≥19.5 μm)d/Λ0.3(Λ≤19.2 μm)d/Λ≥0.0195Λ−0.075(Λ≥19.2 μm)  (C2)

It is preferable that the number of propagation modes of the secondphotonic crystal fiber according to the present invention is three orless in order not to deteriorate the beam quality even in a case whereincident light from a laser oscillator and a mode field diameter of thephotonic crystal fiber are not matched.

Moreover, the second photonic crystal fiber according to the presentinvention enables high power transmission of light and thus does notgenerate output saturation due to stimulated Raman scattering uponpropagation of light of 90 kW·m.

A third photonic crystal fiber according to the present invention is aphotonic crystal fiber having a plurality of holes arranged in theoptical fiber along a longitudinal direction,

in which, in a cross section, a hole ratio which is an area of the holesper unit area is larger in a central side than in an outer side in aportion corresponding to a cladding,

three or more layers having different hole ratios from each other arearranged concentrically with a layer closer to the center having alarger hole ratio,

a diameter d of all the holes are the same, and, when an interval Λbetween a hole in a central layer closest to the center and a hole in anadjacent layer adjacent to the central layer is represented in ahorizontal axis and d/Λ is represented in a vertical axis, Λ and d arein a region where respective regions represented by mathematicalformulas C3 overlap, and

a bending loss of a basic mode is 1 dB/km with a bending radius of 500mm or less.[Mathematical Formulas C3]d/Λ≤0.22Λ−2.01(Λ≤10.9 μm)d/Λ≤−0.000769Λ+0.398(10.9 μm≤Λ≤16.1 μm)d/Λ≤0.004Λ+0.32(Λ≥16.1 μm)d/Λ≥0.00172Λ+0.322(Λ≤15.2 μm)d/Λ≥0.0064Λ+0.250(Λ≥15.2 μm)  (C3)

It is preferable that the number of propagation modes of the thirdphotonic crystal fiber according to the present invention is three orless in order not to deteriorate the beam quality even in a case whereincident light from a laser oscillator and a mode field diameter of thephotonic crystal fiber are not matched.

Moreover, the third photonic crystal fiber according to the presentinvention enables high power transmission of light and thus does notgenerate output saturation due to stimulated Raman scattering uponpropagation of light of 90 kW m.

A fourth photonic crystal fiber according to the present invention is aphotonic crystal fiber having a plurality of holes arranged in theoptical fiber along a longitudinal direction,

in which, in a cross section, a hole ratio which is an area of the holesper unit area is larger in a central side than in an outer side in aportion corresponding to a cladding,

three or more layers having different hole ratios from each other arearranged concentrically with a layer closer to the center having alarger hole ratio,

a diameter d of all the holes are the same, and, when an interval Λbetween a hole in a central layer closest to the center and a hole in anadjacent layer adjacent to the central layer is represented in ahorizontal axis and d/Λ is represented in a vertical axis, Λ and d arein a region where respective regions represented by mathematicalformulas C4 overlap, and

a bending loss of a basic mode is 1 dB/km with a bending radius of 500mm or less.[Mathematical Formulas C4]d/Λ≤0.22Λ−2.01(Λ≤11 μm)d/Λ≤0.407(11 μm≤Λ≤18.7 μm)d/Λ≤0.00333Λ+0.345(Λ≥18.7 μm)d/Λ≥0.00167Λ+0.323(Λ≤14.5 μm)d/Λ≥0.00625Λ+0.255(Λ≥14.5 μm)  (C4)

It is preferable that the number of propagation modes of the fourthphotonic crystal fiber according to the present invention is four orless in order not to deteriorate the beam quality even in a case whereincident light from a laser oscillator and a mode field diameter of thephotonic crystal fiber are not matched.

Moreover, the fourth photonic crystal fiber according to the presentinvention enables high power transmission of light and thus does notgenerate output saturation due to stimulated Raman scattering uponpropagation of light of 90 kW·m.

By allowing a hole structure of a photonic crystal fiber nonuniform inthe range of the mathematical formulas C1 to C4, it is possible toobtain a wide core area while the number of modes that can be propagatedis limited to several. Therefore, the present invention enablesprovision of a photonic crystal fiber in which a wide core area can beobtained with a limited number of propagation modes.

Furthermore, a high-power optical transmission system according to thepresent invention includes a laser oscillator, the photonic crystalfiber, and a coupling part for emitting light from the laser oscillatorto the photonic crystal fiber,

in which, in the coupling part, an amount of misalignment between acentral axis of the light emitted from the laser oscillator and acentral axis of the photonic crystal fiber is 0.95 or less as a relativevalue relative to a mode field radius of the photonic crystal fiber, anda beam radius of the light from the laser oscillator relative to a modefield radius of the photonic crystal fiber is 0.5 or more.

Since an LP01 mode and LP21 have component peaks at positions shiftedfrom the center of the fiber, the coupling efficiency increases whenthere is axis misalignment at a connecting part of the optical fiber.Therefore, by allowing the amount of misalignment between the centralaxis of the light emitted from the laser oscillator and the central axisof the photonic crystal fiber to be 0.95 or less as a relative valuewith respect to the mode field radius of the photonic crystal fiber, thecoupling efficiency between the LP01 mode and LP21 from a laser emittingpart to the photonic crystal fiber can be reduced. Therefore, even whenan effective cross-sectional area of the photonic crystal fiber isenlarged, the power of a propagation mode other than the basic mode canbe reduced, and the beam quality can be enhanced. Therefore, the presentinvention can provide a high-power optical transmission system thatincludes a photonic crystal fiber in which a wide core area can beobtained with a limited number of propagation modes and has a high beamquality.

Advantageous Effects of Invention

The present invention can provide a photonic crystal fiber in which awide core area can be obtained with a limited number of propagationmodes and a high-power optical transmission system including thephotonic crystal fiber and having a high beam quality.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic diagram illustrating an example of an effectiverefractive index distribution of a high-power optical transmissionoptical fiber.

FIG. 2 is a schematic view illustrating an exemplary structure of aphotonic crystal fiber according to the present invention.

FIG. 3 is a schematic view illustrating an exemplary structure of aphotonic crystal fiber according to the present invention.

FIG. 4 is a schematic diagram illustrating an exemplary configuration ofa high-power optical transmission system according to the presentinvention.

FIG. 5 is a characteristic diagram illustrating the coupling efficiencyand the M2 of output light with a higher-order mode with respect tomismatch of beam diameters of incident light and an optical fiber in thehigh-power optical transmission system according to the presentinvention.

FIG. 6 is a characteristic diagram illustrating the coupling efficiencywith an LP11 mode and an LP21 mode due to axis misalignment in thehigh-power optical transmission system according to the presentinvention.

FIG. 7 is a diagram for explaining the relationship between the centerof incident light and the center of an optical fiber in the high-poweroptical transmission system according to the present invention.

FIG. 8 is a diagram for explaining structural conditions in the photoniccrystal fiber according to the present invention.

FIG. 9 is a diagram for explaining structural conditions in the photoniccrystal fiber according to the present invention.

FIG. 10 is a diagram illustrating an example of wavelength dependency ofbending loss in the photonic crystal fiber according to the presentinvention.

FIG. 11 is a diagram for explaining structural conditions in thephotonic crystal fiber according to the present invention.

FIG. 12 is a diagram for explaining structural conditions in thephotonic crystal fiber according to the present invention.

FIG. 13 is a diagram illustrating an example of wavelength dependency ofbending loss in the photonic crystal fiber according to the presentinvention.

FIG. 14 is a characteristic diagram representing the relationshipbetween the allowable bending radius and the effective cross-sectionalarea in the photonic crystal fiber according to the present invention.

FIG. 15 is a characteristic diagram illustrating the relationshipbetween an allowable bending radius and the maximum output power in thephotonic crystal fiber according to the present invention.

FIG. 16 is a schematic view illustrating an exemplary structure of thephotonic crystal fiber according to the present invention.

FIG. 17 is a diagram for explaining structural conditions in thephotonic crystal fiber according to the present invention.

FIG. 18 is a diagram for explaining structural conditions in thephotonic crystal fiber according to the present invention.

FIG. 19 is a diagram for explaining structural conditions in thephotonic crystal fiber according to the present invention.

FIG. 20 is a diagram illustrating an example of wavelength dependency ofbending loss in the photonic crystal fiber according to the presentinvention.

FIG. 21 is a characteristic diagram representing the relationshipbetween the allowable bending radius and the effective cross-sectionalarea in the photonic crystal fiber according to the present invention.

FIG. 22 is a characteristic diagram illustrating the relationshipbetween an allowable bending radius and the maximum output power in thephotonic crystal fiber according to the present invention.

FIG. 23 is a flowchart for explaining an optical fiber design methodaccording to the present invention.

DESCRIPTION OF EMBODIMENTS

Embodiments of the present invention will be described with reference tothe accompanying drawings. The embodiments described below are examplesof the present invention, and the present invention is not limited tothe following embodiments. Note that components having the same symbolin the present description and the drawings represent items identical toeach other.

First Embodiment

FIG. 1 is an example of an effective refractive index distribution in ahigh-power optical transmission optical fiber. In the present opticalfiber, by arranging a layer having a refractive index lower than that ofan outer cladding region around a core region, a trade-off betweenenlargement of a core area and reduction in the number of modes isimproved, thus implementing both higher quality and higher power ofoutput light in high-power optical transmission. Particularly in thisembodiment, in order to implement control of fine refractive indexdifference, a plurality of holes is arranged in a uniform quartz glass,and the arrangement and/or the size of the holes are controlled for eachlayer, thereby implementing the effective refractive index distributionillustrated in FIG. 1.

A photonic crystal fiber of the present embodiment has a plurality ofholes arranged in the optical fiber along a longitudinal direction, inwhich, in a cross section, a hole ratio which is an area of the holesper unit area is larger in a central side than in an outer side in aportion corresponding to a cladding, and the number of propagation modesin which propagation is possible is 3 or less.

FIG. 2 is an exemplary structure 1 of a photonic crystal fiber as ahigh-power optical transmission optical fiber. In the photonic crystalfiber of FIG. 2, holes 11 are arranged in quartz 12 in a hexagonalclose-packed manner with a hole interval Λ, and a core region is formedby not arranging holes in a region corresponding to seven holes in thecenter of the optical fiber. Moreover, only holes of the first layeradjacent to the core region have a hole diameter d1 larger than a holediameter d of holes arranged on an outer side thereof. By setting d1>d,an effective refractive index of the first layer becomes lower than thatof a hole layer on an outer side thereof, thereby the refractive indexdistribution illustrated in FIG. 1 is implemented.

FIG. 3 is an exemplary structure 2 of a photonic crystal fiber as ahigh-power optical transmission optical fiber. In the photonic crystalfiber of FIG. 3, a plurality of holes 11 having a constant diameter d isarranged in quartz 12 in a plurality of hexagonal shapes. Like in FIG.2, a core region is formed in the center by not arranging holes in aregion corresponding to seven holes in the center of the optical fiber.In the structure of FIG. 3, a distance Λ1 between adjacent holes in thefirst layer adjacent to the core region is smaller than a distance Λbetween holes in hole layers on an outer side thereof. By setting Λ1<Λ,a hole density of the first layer becomes higher than that of the outerside, thereby the refractive index distribution illustrated in FIG. 1 isimplemented. Here, since the size of the holes are all constant in thestructure of FIG. 3, it is unnecessary to perform size control for eachhole at the time of manufacturing a base material and spinning theoptical fiber, and thus the manufacturing process is relatively simpleand thus is preferable as compared with the structure of FIG. 2.

FIG. 4 illustrates an exemplary configuration of a transmission system81 to which a high-power optical transmission optical fiber 91 of thepresent invention is applied. Included are a laser oscillator 92 foremitting high output light and a lens 93 for allowing the output lightto be focused on the center of a core region of the optical fiber andemitting the light. Here, a workpiece 82 is arranged at an output partof the optical fiber and subjected to processing such as cutting, and asthe beam quality M2 of output light of the optical fiber is closer to 1,the accuracy and efficiency of processing can be much more improved.

In FIG. 5, the coupling efficiency with a basic mode (LP01) and LP11,LP21, and LP02 modes are illustrated with respect to mismatch of modefield diameters (MFDs) of incident light and a transmission opticalfiber (MFD of incident light/MFD of the fiber). In the absence ofmismatch of the MFDs, the beam quality is not deteriorated since incoupling to the LP01 mode is entirely implemented under ideal conditionswithout disturbance such as axis misalignment; however, in general, aperfect match of MFDs of the laser oscillator and the transmissionoptical fiber is extremely rare. Even in a case where there is an MFDmismatch, the coupling efficiency with the LP11 and the LP21 modes is asquite small as 5% or less. This is because electric field distributionsof both modes do not have a component near the center thereof, and thuscoupling with incident light does not occur. On the other hand, in theLP02 mode having an electric field distribution similar to that of thebasic mode, the coupling efficiency increases along with the MFDmismatch, which increases the value of M2 illustrated on the verticalaxis on the right side, thereby deteriorating the beam quality.Therefore, in the high-power transmission optical fiber and thetransmission system of the present invention, in order to avoiddeterioration of the beam quality of output light, by adopting aphotonic crystal fiber having a structure in which the LP02 mode is notpropagated, it is possible to stably obtain output light of a highquality independently of the degree of an MFD mismatch between the laseroscillator and the transmission optical fiber. Furthermore even in acase where the LP02 mode can be propagated, when a ratio between a beamdiameter of incident light and an MFD of the optical fiber is 0.5 ormore as illustrated in FIG. 5, M2 is 2 or less, and thus output light ofa high quality can be obtained.

FIG. 6 illustrates the coupling efficiency of the LP11 and the LP21modes and the change in M² with respect to axis misalignment. Thehorizontal axis represents a relative value of the amount of axismisalignment from the center with respect to the mode field radius ofthe LP01 mode of the fiber. Since the LP11 and the LP21 modes have apeak at a position shifted from the center of the fiber, the couplingefficiency of these higher order modes is increased by axismisalignment, and as a result, the beam quality is deteriorated. Inorder to avoid deterioration of the output light beam quality (increasein M²) by these higher order modes, for example in order to allow M² tobe 2.0 or less, it is necessary to set the amount of relative axismisalignment to 0.95 or less. Therefore in the high-power opticaltransmission system of the present invention, by controlling the amountof axis misalignment between the center axis of the laser oscillator,that is, an optical axis of output light of the laser oscillator and thecentral axis of the photonic crystal fiber at a coupling part 94 to be0.95 or less relative to the mode field the radius of the transmissionoptical fiber as illustrated in FIG. 7, it is possible to obtainextremely high-quality output light with an M² of 2.0 or less.

In FIG. 8, structural conditions of the high-power optical transmissionoptical fiber of the present invention using the structure illustratedin FIG. 2 are illustrated. Note that the structural conditions have beenobtained by numerical calculation analysis. The figure illustratesstructural conditions at a wavelength of 1.06 μm, and a solid line inthe figure is obtained by calculating and plotting structural conditionsunder which a loss with respect to the LP02 mode is 0.1 dB/m, and theLP02 mode is not propagated in a region under the solid line. A brokenline is obtained by calculating and plotting structural conditions underwhich a bending loss in the basic mode is 1 dB/km at a bending radius Rillustrated in the figure, and the bending loss in the basic mode can besufficiently lowered in a region in the left from the broken line, and ahigh-power optical transmission optical fiber and an optical fiber cablewith a low loss can be obtained.

Here, the maximum value of output light power can be increased byenlarging an effective cross-sectional area of the basic mode, and theeffective cross-sectional area can be enlarged by increasing theinter-hole interval Λ of the PCF. Therefore, at an intersection of thesolid line and the broken line, propagation in the LP02 mode andincrease in the bending loss can be simultaneously prevented, and theeffective cross-sectional area can be maximized at a bending radiuscorresponding to the broken line.

Here, the relationship between the maximum value of output light power(maximum output power) and the effective cross-sectional area of thebasic mode will be described. The maximum output power P_(th) isdetermined by an output power limit (stimulated Raman threshold) due tostimulated Raman scattering out of the nonlinearity and is expressed bythe following mathematical formula.

[Mathematical  Formula  C5] $\begin{matrix}{P_{th} = \frac{16A_{eff}}{g_{R}L}} & ({C5})\end{matrix}$

Note that the above mathematical formula is widely known as amathematical formula for deriving a saturation threshold of output powerby the stimulated Raman including Non-Patent Literature 4, where g_(R)represents a Raman gain coefficient, Aeff represents an effectivecross-sectional area, and L represents a transmission distance.

Leff can be derived from a transmission loss a and the transmissiondistance L by Leff=(1−exp(αL))α, however in a case where thetransmission distance is relatively short such as about 1 km or less,Leff and L can be regarded as equivalent. Therefore, as a high-powertransmission performance, a product P_(th)·L of the induced Ramanthreshold P_(th) and the transmission distance L which is a parameterproportional to Aeff can be used. Note that, according to Non-PatentLiterature 4, in the case of pure quartz, gR is about 1.0 e⁻¹³ m/W at awavelength of 1.06 μm. For example, where Aeff is 500 pmt, thehigh-power transmission performance P_(th)·L is about 90 kW·m.

Furthermore, structural conditions under which the effectivecross-sectional area is a predetermined value is illustrated by a dottedline in FIG. 8. The effective cross-sectional area relates to an outputof laser and a propagation distance of the optical fiber. For example,in general, a laser output used as an industrial laser is about 300 W,and assuming remote control of about 300 m, 90 kW·m is obtained. Aneffective cross-sectional area Aeff of an optical fiber that allowslight of 90 kW·m to be propagated can be derived by the stimulated Ramanthreshold and is about 500 μm². A leftmost dotted line illustrated inFIG. 8 is a line for an effective cross-sectional area Aeff=500 μm², anda right side of the dotted line is a region where light of 90 kW·m ormore can be propagated.

In FIG. 9, a region approximating, by a polygon, a region surrounded bya plurality of linear functions (solid line, broken line, dotted line)with respect to the structural conditions illustrated in FIG. 8 isillustrated. From FIG. 9, a high-power transmission optical fiber havingthe structure of FIG. 2 that satisfies requirements of 90 kW·m or more,three or less propagation modes, and a bending radius of 500 mm or lessis given by the C1.[Mathematical Formulas C1]d1/d≤0.633Λ−5.467(Λ11.8 μm)d1/d≤−0.0429Λ+2.486(11.8 μm≤Λ15.4 μm)d1/d≥0.0454Λ1.13(Λ≥15.4 μm)d1/d≥1(Λ≤16.8 μm)d1/d≥0.117Λ−0.96(Λ≥16.8 μm)  (C1)

FIG. 10 illustrates an example of wavelength dependency of the bendingloss in the structure illustrated in FIG. 2. Here, it is assumed thatΛ=20 μm, d/Λ=0.35, and d1/d=1.71 hold with a bending radius of 400 mm.As illustrated in the figure, a change in the bending loss in thewavelength range of 1.06±0.01 μm is sufficiently small. Generally, YAGlasers used as high-output lasers are known to have a central wavelengthof approximately 1.06 μm, and as illustrated in FIG. 10 the wavelengthdependency of the bending loss near the central wavelength of a YAGlaser is sufficiently small, it is clear that a design range derivedusing FIG. 8 or 9 is effective in a wavelength range of 1.05 to 1.07 μm.

Note that, in general, it is known that the bending loss of a PCFincreases more as the wavelength becomes shorter, and it is obvious thatthe bending loss becomes further smaller as the wavelength becomeslonger than 1.07 μm.

In FIG. 11, structural conditions of the high-power optical transmissionoptical fiber of the present invention using the structure illustratedin FIG. 3 are illustrated. Meanings of a solid line, broken lines, anddotted lines in FIG. 11 are the same as those in FIG. 8, and at anintersection of the solid line and a broken line, propagation in theLP02 mode and increase in the bending loss can be simultaneouslyprevented, and the effective cross-sectional area can be maximized at abending radius corresponding to the broken line.

In FIG. 12, a region approximating, by a polygon, a region surrounded bya plurality of linear functions (solid line, broken line, dotted line)with respect to the structural conditions illustrated in FIG. 11 isillustrated. From FIG. 12, a high-power transmission optical fiber ofthe present invention having the structure of FIG. 3 that satisfiesrequirements of 90 kW·m or more, three or less propagation modes, and abending radius of 500 mm or less is given by the C2.[Mathematical Formulas C2]d/Λ≤0.24Λ−2.22(Λ≤10.8 μm)d/Λ≤0.00667Λ+0.293(10.8 μm≤Λ≤19.5 μm)d/Λ≤0.01Λ+0.23(Λ≥19.5 μm)d/Λ≥0.3(Λ≤19.2 μm)d/Λ≥0.0195Λ−0.075(Λ≥19.2 μm)  (C2)

FIG. 13 illustrates an example of wavelength dependency of the bendingloss in the structure illustrated in FIG. 3. Here, it is assumed thatA=20 μm and d/Λ=0.45 hold with a bending radius of 300 mm. Asillustrated in the figure, a change in the bending loss in thewavelength range of 1.06±0.01 μm is sufficiently small, and it is clearthat design conditions derived using FIG. 11 or 12 are effective as sameas in FIG. 10 in the above wavelength range.

FIG. 14 illustrates the relationship between the allowable bendingradius and the effective cross-sectional area of the high-power opticaltransmission optical fiber of the present invention. Here, like theabove, the allowable bending radius is a bending radius at which thebending loss is 1 dB/km or less with light having a wavelength of 1.06μm propagated in the LP01 mode. Moreover, FIG. 15 illustrates therelationship between the allowable bending radius and the maximum outputlight power standardized by the transmission distance of the high-poweroptical transmission optical fiber of the present invention. Plots of“circle” and “quadrangle” in the figure represent the structures ofFIGS. 2 and 3, respectively, and represent values at intersections ofthe solid line and the broken line in FIGS. 8 and 11, respectively. FromFIG. 15, it is possible to enlarge an obtained effective cross-sectionalarea by relaxing the allowable bending radius, and changing theallowable bending radius from 100 mm to 500 mm allows the effectivecross-sectional area to be enlarged from 700 μm² to 3600 μm² at themaximum.

There is a certain correlation between the effective cross-sectionalarea Aeff and the allowable bending radius R, and assuming MathematicalFormula 1 using proportional coefficients a and b results in a highcorrelation with the result of FIG. 14.[Mathematical Formula 1]Aeff≤aR ^(b)  (1)

For example in FIG. 14, a=14.9 and b=0.85 hold in the structure of FIG.2, and a=7.27 and b=1.01 hold in the structure of FIG. 3, and in theregion having an allowable bending radius of 500 mm or less, the maximumeffective cross-sectional area obtained for a predetermined bendingradius is approximately proportional to the allowable bending radius. Acorrelation coefficient representing the approximate accuracy for eachof the above is 0.98 or more, which shows that the approximation of themathematical formula (1) is effective for design of a PCF in ahigh-power optical transmission optical fiber. Therefore, by using themathematical formula (1), it is possible to design a required bendingradius with respect to a desired output light power, that is, aneffective cross-sectional area.

For example, by using a PCF obtained by the structure design describedabove, in the case of transmission of about 50 m as illustrated in FIG.15, an output of 2 kW or more can be obtained even under severeconditions such as an allowable bending radius of 100 mm or less, andincreasing the allowable bending radius up to 400 mm enables obtainingan output of 10 kW or more. Moreover, it can be confirmed thathigh-power light of 1 kW or more can be transmitted over a long distanceof 300 m or more by setting the allowable bending radius to about 200 to300 mm.

Second Embodiment

In a PCF of the present embodiment, three or more layers havingdifferent ratios of holes 11 from each other are arranged concentricallywith a layer closer to the center has a larger ratio of the holes 11,and the number of propagation modes that can propagate is 4 or less.

FIG. 16 illustrates an exemplary structure of a high-power opticaltransmission optical fiber of the present invention. In the structure ofFIG. 16, the diameter of all the holes are the same, and the holes arearranged such that and the refractive index is increased stepwise from ahole layer adjacent to a core region toward an outer side. As a result,it is possible to increase a leakage loss in a higher-order mode whilethe bending loss with a basic mode is mitigated and to further improvethe trade-off between enlargement of a core area and reduction in thenumber of modes. In FIG. 16, by arranging holes in a first layer, asecond layer, and a third layer at hole intervals Λ and increasing thehole density in each of the hole layers more in a layer closer to thecenter, the refractive index distribution described above isimplemented. As a result, it is possible to further improve thetrade-off between enlargement of a core area and reduction in the numberof propagation modes with a smaller number of holes than that of thestructure illustrated in FIG. 3, and since the size of the holes isconstant, difficulty in manufacture can be preferably mitigated.

In FIG. 17, structural conditions of the high-power optical transmissionoptical fiber of the present invention using the structure illustratedin FIG. 16 are illustrated. In the figure, structural conditions at awavelength of 1.06 μm are illustrated, and two solid lines in the figureillustrate structures in which the LP02 mode and the LP31 mode arenon-propagating. That is, the number of propagation modes is 4 in aregion under a solid line of a non-propagation condition of the LP31mode, and the number of propagation modes is 3 in a region under a solidline of a non-propagation condition of the LP02 mode. A broken linerepresents a structural condition under which a bending loss of thebasic mode is 1 dB/km at a bending radius R illustrated in the figure.Also, a dotted line represents a structural condition under which theeffective cross-sectional area is a predetermined value (a valuedetermined by power and the propagation distance of a laser).

In FIG. 18, a region approximating, by a polygon, a region surrounded bya plurality of linear functions (solid line, broken line, dotted line)with respect to the structural conditions under which the number ofpropagation modes is 3 or less illustrated in FIG. 17 is illustrated.From FIG. 18, a high-power transmission optical fiber having thestructure of FIG. 16 that satisfies requirements of 90 kW·m or more,three or less propagation modes, and a bending radius of 500 mm or lessis given by the C3.[Mathematical Formulas C3]d/Λ≤0.22Λ−2.01(Λ≤10.9 μm)d/Λ≤−0.000769Λ+0.398(10.9 μm≤Λ≤16.1 μm)d/Λ≤0.004Λ+0.32(Λ≥16.1 μm)d/Λ≥0.00172Λ+0.322(Λ≤15.2 μm)d/Λ≥0.0064Λ+0.250(Λ≥15.2 μm)  (C3)

In FIG. 19, a region approximating, by a polygon, a region surrounded bya plurality of linear functions (solid line, broken line, dotted line)with respect to the structural conditions under which the number ofpropagation modes is 4 or less illustrated in FIG. 17 is illustrated.From FIG. 19, a high-power transmission optical fiber having thestructure of FIG. 16 that satisfies requirements of 90 kW·m or more,four or less propagation modes, and a bending radius of 500 mm or lessis given by the C4.[Mathematical Formulas C4]d/Λ≤0.22Λ−2.01(Λ≤11 μm)d/Λ≤0.407(11 μm≤Λ≤18.7 μm)d/Λ≤0.00333Λ+0.345(Λ≥18.7 μm)d/Λ≥0.00167Λ+0.323(Λ≤14.5 μm)d/Λ≥0.00625Λ+0.255(Λ≥14.5 μm)  (C4)

FIG. 20 illustrates an example of wavelength dependency of the bendingloss in the structure illustrated in FIG. 16. Here, it is assumed thatA=20 μm and d/Λ=0.45 hold with a bending radius of 300 mm. Asillustrated in the figure, a change in the bending loss in thewavelength range of 1.06±0.01 μm is sufficiently small, and it is clearthat design conditions derived using FIGS. 17 to 19 are effective likein FIG. 10 in the above wavelength range.

FIG. 21 illustrates the relationship between the allowable bendingradius and the effective cross-sectional area of the high-power opticaltransmission optical fiber of the present invention. Here, like theabove, the allowable bending radius is a bending radius at which thebending loss is 1 dB/km or less with light having a wavelength of 1.06μm propagated in the LP01 mode. Moreover, FIG. 22 illustrates therelationship between the allowable bending radius and the maximum outputlight power standardized by the transmission distance of the high-poweroptical transmission optical fiber of the present invention. Plots of“circle” and “quadrangle” in the figure represent the case of threepropagation modes and the case of four propagation modes propagated inthe structure of FIG. 16, respectively, which are values ofintersections of the solid line and the broken line in FIG. 17.

FIGS. 21 and 22 illustrate the effective cross-sectional area and themaximum output power, respectively, in the structures at theintersections of the solid line and the broken line in FIG. 17. Also inthese structures, by reducing the allowable bending radius to 500 mm,the effective cross-sectional area can be enlarged up to 3500 pmt, andthe maximum output power can be increased to 10 kW or more with atransmission distance of 50 m, for example. Furthermore, by allowing thenumber of propagation modes up to be 4, it is possible to increase themaximum effective cross-sectional area and the maximum output power byabout 10%. Since the LP02 mode can be propagated at this time, it ispreferable that the diameter of an incident light beam is 0.5 or morerelative to an MFD of the optical fiber in order to preventdeterioration of M2.

Third Embodiment

FIG. 23 is a flowchart illustrating an example of a design procedure ofthe high-power optical transmission optical fiber of the presentinvention. Performed in a photonic crystal fiber design method of thepresent embodiment is:

a specification value determining step of determining a wavelength oflight propagated in the photonic crystal fiber, power P_(th) of thelight propagated in the photonic crystal fiber, and a propagationdistance L through which the light is propagated in the photonic crystalfiber;

an effective cross-sectional area calculating step of calculating arequired effective cross-sectional area A_(eff) of the photonic crystalfiber by utilizing a mathematical formula C5 on the basis of the powerP_(th) and the propagation distance L having been determined in thespecification value determining step and a Raman gain coefficient g_(R);

a hole structure detecting step of calculating an effectivecross-sectional area A_(eff) from a diameter d and an interval Λ of theholes of the photonic crystal fiber, and detecting the diameter d andthe interval Λ of the holes of the A_(eff) satisfying or exceeding therequired A_(eff) having been calculated in the effective cross-sectionalarea calculating step on the basis of a plotted graph having ahorizontal axis of d/Λ and a vertical axis of Λ;

a bending radius determining step of determining a region of allowablebending radius with which a basic mode can be propagated in the photoniccrystal fiber;

a region detecting step of detecting an overlapping region in which anon-propagating region in which the LP02 mode or the LP31 mode is notpropagated, a region of the allowable bending radius having beendetermined in the bending radius determining step, and a region based ona product of power of light from a laser oscillator and the propagationdistance L overlap in a graph representing the interval Λ of the holeson a horizontal axis and a ratio (d1/d) of a diameter d1 of the holes onthe central side and the diameter d of holes adjacent to the holes inthe central side from the outer side thereof on a vertical axis or in agraph representing the interval Λ of the holes adjacent to the holes inthe central side from the outer side thereof on a horizontal axis and aratio (d/Λ) of the diameter d and the interval Λ of the holes on avertical axis; and a structure determining step of determining theinterval Λ and the ratio (d1/d) or the interval Λ and the ratio (d/Λ) inthe overlapping region as a structure of the photonic crystal fiber.

In a specification value determining step S01, the wavelength, thetransmission distance, and the output power P_(th) are set asparameters. In an effective cross-sectional area calculating step S02,an effective cross-sectional area is calculated by the mathematicalformula (C5) on the basis of the specifications having been set. Notethat theoretically, L in the mathematical formula (C5) can be replacedby the interaction length defined by Leff=(1−exp(αL))/α; however, sinceit is assumed that the optical fiber of the present invention has arelatively short transmission distance such as 1 km or less, and Leffand L are equivalent values, the transmission distance L is used. Notethat the transmission distance is not limited to 1 km or less and can besimilarly applied as long as Leff and L can be regarded as equivalent.

In a hole structure detecting step S03, a hole structure giving thecalculated effective cross-sectional area is detected. Specifically, astructure such as that of FIG. 2, FIG. 3, or FIG. 16 is determined, andthe effective cross-sectional area Aeff is previously calculated using Λand d as parameters and plotted as illustrated in FIG. 8. Then, usingFIG. 8, ranges of Λ and d satisfying the effective cross-sectional areaAeff having been calculated in the effective cross-sectional areacalculating step S02 is found. In a bending radius determining step S04,a desired allowable bending radius is set.

In a region detecting step, steps from S05 to S07 are performed.

In step S05, the bending loss in the LP01 mode at the allowable bendingradius having been set in the bending radius determining step S04 in thePCF having the hole structure detected in the hole structure detectingstep S03 is calculated (for example, the bending loss in the LP01 modeis in the range of 1 dB/km or less, and a left side region of a brokencurve in FIG. 8, FIG. 11, or FIG. 17 is determined). Here, a regionsatisfying a product of the output power the distance explained in FIG.9 or FIG. 12 is also set. Furthermore, it is confirmed that the holestructure detected in the hole structure detecting step S03 is includedin the overlapping portion of the regions. If the hole structure isincluded in the overlapping portion of the regions (“Yes” in step SOS),step S06 is performed. Note that if the hole structure is not includedin the overlapping portion of the regions (“No” in step S05), the flowreturns to the bending radius determining step S04 to set a largeallowable bending radius, and the design flow is advanced. Note that, inthis step, in order to determine whether the bending loss at theallowable bending radius is appropriate, the relationship between theeffective cross-sectional area and the bending radius expressed by themathematical formula (1) can be used. That is, if the set allowablebending radius and the effective cross-sectional area satisfy themathematical formula (1), the flow is advanced, and if not satisfyingthe mathematical formula (1), the process returns to step S04 to set alarge allowable bending radius.

If the hole structure is included in the region in which the conditionof the number of propagation modes is 3 or less, that is, the regionunder the solid line of the LP02 mode non-propagation condition in FIG.8, 11, or 17 (for example, a loss of 0.1 dB/m or more) (“Yes” in stepS06), the hole structure is employed (step S08). If a structure havingthree or less modes cannot be obtained (“No” in step S06), if the holestructure is included in the region in which the condition of the numberof propagation modes is 4 or less, that is, the region under the solidline of the LP31 mode non-propagation condition in FIG. 8, 11, or 17(“Yes” in step S07), the hole structure is employed (step S08). On theother hand, if the structure does not have four modes or less (“No” instep S07), the flow returns to the specification value determining stepS01 to reduce either one or both of the transmission distance and theoutput power, and the design flow is performed again.

Noted that the three propagation modes refer to the LP01 mode, the LP11mode, and the LP21 mode, and the four propagation modes refer to theLP01 mode, the LP11 mode, the LP21 mode, and the LP02 mode.

INDUSTRIAL APPLICABILITY

The PCF according to the present invention can be applied to industrialprocessing using high-power light.

REFERENCE SIGNS LIST

-   11 Hole-   12 Quartz-   81 High-power optical transmission system-   82 Workpiece-   91 PCF-   92 Laser oscillator-   93 Lens-   94 Coupling part

The invention claimed is:
 1. A photonic crystal fiber having a plurality of holes arranged in the photonic crystal fiber along a longitudinal direction, wherein, in a cross section, a hole ratio which is an area of the holes per unit area is larger in a central side than in an outer side in a portion corresponding to a cladding, a diameter d is the same for all of the holes, and an interval Λ1 of the holes in the central side is smaller than an interval Λ of the holes in the outer side, and, when Λ is represented in a horizontal axis and d/Λ is represented in a vertical axis, A and d are in a region where respective regions represented by mathematical formulas C2 overlap, and wherein the photonic crystal fiber propagates light of 90 kW·m or more, has an effective cross-sectional area of 500 μm² or more, and has a bending loss of a basic mode of 1 dB/km with a bending radius of 500 mm or less for a wavelength range of 1.05 to 1.07 μm $\begin{matrix} \left\lbrack {{Mathematical}\mspace{14mu}{Formulas}\mspace{14mu} C\; 2} \right\rbrack & \; \\ \begin{matrix} {{d/\Lambda} \leq {{0.24\Lambda} - 2.22}} & \left( {\Lambda \leqq {10.8\mspace{14mu}{\mu m}}} \right) \\ {{d/\Lambda} \leq {{0.00667\Lambda} + 0.293}} & \left( {{10.8\mspace{14mu}{\mu m}} \leqq \Lambda \leqq {19.5\mspace{14mu}{\mu m}}} \right) \\ {{d/\Lambda} \leq {{0.01\Lambda} + 0.23}} & \left( {\Lambda \geq {19.5\mspace{14mu}{\mu m}}} \right) \\ {{d/\Lambda} \geq 0.3} & \left( {\Lambda \leqq {19.2\mspace{14mu}{\mu m}}} \right) \\ {{d/\Lambda} \geq {{0.0195\Lambda} - 0.075}} & {\left( {\Lambda \geq {19.2\mspace{14mu}{\mu m}}} \right).} \end{matrix} & \left( {C\; 2} \right) \end{matrix}$
 2. The photonic crystal fiber according to claim 1, wherein the number of propagation modes is three or less.
 3. A photonic crystal fiber having a plurality of holes arranged in the photonic crystal fiber along a longitudinal direction, wherein, in a cross section, a hole ratio which is an area of the holes per unit area is larger in a central side than in an outer side in a portion corresponding to a cladding, three or more layers having different hole ratios from each other are arranged concentrically with a layer closer to a center having a larger hole ratio, a diameter d is the same for all of the holes, and, when an interval Λ between a hole in a central layer closest to the center and a hole in an adjacent layer adjacent to the central layer is represented in a horizontal axis and d/Λ is represented in a vertical axis, Λ and d are in a region where respective regions represented by mathematical formulas C3 overlap, and wherein the photonic crystal fiber propagates light of 90 kW·m or more, has an effective cross-sectional area of 500 μm² or more, and has a bending loss of a basic mode of 1 dB/km with a bending radius of 500 mm or less for a wavelength range of 1.05 to 1.07 μm $\begin{matrix} {\left\lbrack {{Mathematical}\mspace{14mu}{Formulas}\mspace{14mu} C\; 3} \right\rbrack\mspace{419mu}} & \; \\ \begin{matrix} {{d/\Lambda} \leq {{0.22\Lambda} - 2.01}} & \left( {\Lambda \leqq {10.9\mspace{14mu}{\mu m}}} \right) \\ {{d/\Lambda} \leq {{{- 0.000769}\Lambda} + 0.398}} & \left( {{10.9\mspace{14mu}{\mu m}} \leqq \Lambda \leqq {16.1\mspace{14mu}{\mu m}}} \right) \\ {{d/\Lambda} \leq {{0.004\Lambda} + 0.32}} & \left( {\Lambda \geq {16.1\mspace{14mu}{\mu m}}} \right) \\ {{d/\Lambda} \geq {{0.00172\Lambda} + 0.322}} & \left( {\Lambda \leqq {15.2\mspace{14mu}{\mu m}}} \right) \\ {{d/\Lambda} \geq {{0.0064\Lambda} + 0.250}} & {\left( {\Lambda \geq {15.2\mspace{14mu}{\mu m}}} \right).} \end{matrix} & \left( {C\; 3} \right) \end{matrix}$
 4. The photonic crystal fiber according to claim 3, wherein the number of propagation modes is three or less.
 5. A photonic crystal fiber having a plurality of holes arranged in the photonic crystal fiber along a longitudinal direction, wherein, in a cross section, a hole ratio which is an area of the holes per unit area is larger in a central side than in an outer side in a portion corresponding to a cladding, three or more layers having different hole ratios from each other are arranged concentrically with a layer closer to a center having a larger hole ratio, a diameter d is the same for all of the holes, and, when an interval Λ between a hole in a central layer closest to the center and a hole in an adjacent layer adjacent to the central layer is represented in a horizontal axis and d/Λ is represented in a vertical axis, Λ and d are in a region where respective regions represented by mathematical formulas C4 overlap, and wherein the photonic crystal fiber propagates light of 90 kW·m or more, has an effective cross-sectional area of 500 μm² or more, and has a bending loss of a basic mode of 1 dB/km with a bending radius of 500 mm or less for a wavelength range of 1.05 to 1.07 μm $\begin{matrix} {\left\lbrack {{Mathematical}\mspace{14mu}{Formulas}\mspace{14mu} C\; 4} \right\rbrack\mspace{419mu}} & \; \\ \begin{matrix} {{d/\Lambda} \leq {{0.22\Lambda} - 2.01}} & \left( {\Lambda \leqq {11\mspace{14mu}{\mu m}}} \right) \\ {{d/\Lambda} \leq 0.407} & \left( {{11\mspace{14mu}{\mu m}} \leqq \Lambda \leqq {18.7\mspace{14mu}{\mu m}}} \right) \\ {{d/\Lambda} \leq {{0.00333\Lambda} + 0.345}} & \left( {\Lambda \geq {18.7\mspace{14mu}{\mu m}}} \right) \\ {{d/\Lambda} \geq {{0.00167\Lambda} + 0.323}} & \left( {\Lambda \leqq {14.5\mspace{14mu}{\mu m}}} \right) \\ {{d/\Lambda} \geq {{0.00625\Lambda} + 0.255}} & {\left( {\Lambda \geq {14.5\mspace{14mu}{\mu m}}} \right).} \end{matrix} & \left( {C\; 4} \right) \end{matrix}$
 6. The photonic crystal fiber according to claim 5, wherein the number of propagation modes is four or less. 